These last two results exhibit some interesting facts. The solutions given by Theorem REF  are least energy solutions to the system (REF ) having some specific symmetries described in Example REF \((ii)\)  below. Their components behave as expected in the repulsive case \(\lambda _{ij}<0\) , i.e., they concentrate at points that are far from each other and from the boundary of the ball. On the other hand, the solutions given by Theorem REF  behave as shown by Lin and Wei [1]} for the attractive case \(\lambda _{ij}>0\) , i.e., all components concentrate at the origin. The solutions given by Theorem REF  enjoy the same symmetries as those given by Theorem REF  (and more), but they have higher energy. This shows that the sign of the interaction coefficient \(\lambda _{ij}\)  is not determinant in the segregation behavior of higher energy solutions.
